Classical X-ray sources that are used for example in medical X-ray diagnostics comprise a heated cathode for emitting electrons towards an anode, where the bombardment with electrons generates X-ray beams. Moreover, the U.S. Pat. No. 6,912,268 B2 describes an X-ray source with a single “cold cathode” that has a curved surface from which electrons are emitted such that they converge onto the associated anode.